Theorem ancoms 54

Description: Swap the two elements of a context. (Contributed by Mario Carneiro, 8-Oct-2014.)

Hypothesis

Ref	Expression
ancoms.1	⊢ (R, S)⊧T

Assertion

Ref	Expression
ancoms	⊢ (S, R)⊧T

Proof of Theorem ancoms

Step	Hyp	Ref	Expression
1		ancoms.1	. . . . 5 ⊢ (R, S)⊧T
2	1	ax-cb1 29	. . . 4 ⊢ (R, S):∗
3	2	wctr 34	. . 3 ⊢ S:∗
4	2	wctl 33	. . 3 ⊢ R:∗
5	3, 4	simpr 23	. 2 ⊢ (S, R)⊧R
6	3, 4	simpl 22	. 2 ⊢ (S, R)⊧S
7	5, 6, 1	syl2anc 19	1 ⊢ (S, R)⊧T

Syntax hints:  kct 10  ⊧wffMMJ2 11

This theorem was proved from axioms:  ax-syl 15  ax-jca 17  ax-simpl 20  ax-simpr 21  ax-cb1 29  ax-wctl 31  ax-wctr 32

This theorem is referenced by:  adantl  56  anasss  61